Electrochemical Kinetics by Faradaic Impedance - American Chemical

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8204

J. Phys. Chem. 1989, 93, 8204-8212

Ion Transfer across Liquid-Liquid Phase Boundaries: Electrochemical Kinetics by Faradaic Impedance Thomas Wandlowski,+Vladimir MareZek, Karel Holub, and Zdenek Samec* J . Heyrovskj Institute of Physical Chemistry and Electrochemistry, Czechoslovak Academy of Sciences, DolejSkova 3, 182 23 Prague 8, Czechoslovakia (Received: September 6, 1988; In Final Form: April 27, 1989)

Ion transport rates across the water-nitrobenzene interface have been determined by faradaic impedance measurements at equilibrium potentials. Lithium chloride’and tetrabutylammonium tetraphenylborate (or tetraphenylarsonium dicarbollylcobaltate) were used as supporting electrolytes. First-order ion-transfer kinetics across the phase boundary were substantiated for bulky anions and cations. The potential dependence of the relevant heterogeneousrate constants was similar to the classical Butler-Volmer equation for conventional electrochemical rate constants. This finding is accounted for by a three-step mechanism. Ion transfer across a rigid layer of solvent molecules at the phase boundary was the rate-determining step. That compact layer was “sandwiched” between two space charge layers and presented a potential barrier of 14-17 kJ mol-I. Based on these results, limiting rates were estimated for the solvent extraction of picrates and perchlorates from water into nitrobenzene.

Introduction Liquid-liquid interfacial kinetics has attracted much attention in the recent past.’ Work has been focused on the simple transfer of soluble solutes from the aqueous to the organic (oil) phase or vice versa solute (w) s solute (0) (1) eventually assisted by an oil-soluble complexing agent.lS2 Theoretical models and methods for kinetic measurements were reviewed and their applicability discussed.2 One of the more sophisticated approaches to the study of the interfacial kinetics has been through direct measurements of the ion-transfer rates across the interface between two immiscible electrolyte solutions (ITIES) by various electrochemical technique^.^ We have been interested in using cyclic4 or convolution potential sweep5 voltammetry for this purpose. Others have employed galvanostatic pulse,6 phase-selective ac polarographic’ or faradaic impedance8 techniques. However, the evaluation of ion-transfer rates from measurements involving large potential sweeps and variations can be uncertain. This is mainly because of the considerable ohmic potential drop, which must be compensated or subtracted in potentiostatic or galvanostatic experiments. Moreover, mechanical instabilities of the ITIES arising from the potential dependence of the surface tension9 can influence the ion transport. For these reasons, the application of a small signal exciting the system in the thermodynamic equilibrium should offer more reliable kinetic data.1° Unfortunately, data obtained in this way are few and inconsistent. Impedance measurements of the equilibrium pictrate ion transfer across the water-nitrobenzene interfacelo indicated that ionic rate constants can be as high as about 0.1 cm s-l. Consequently, those evaluated from direct current m e a ~ u r e m e n t s ~ ~ are underestimated by a factor 2 or 3. On the other hand, ionic rate constants as low as about 5 X cm s-I have been reported for some tetraalkylammonium ions and perchlorate.8 I n the present paper we aim at a better understanding of the mechanism of the ion transport across the ITIES. For this purpose, the transfer of series of monovalent (tetraalkylammonium, tetraalkylphosphonium) and divalent (dialkyldipyridinium) cations and of perchlorate anion was studied by an equilibrium impedance technique. As compared with literature data, the present results definitely point to a faster (and in some cases distinctly faster) ion transport kinetics. These results are of consequence for the analysis of the molecular mechanism of the ion transport as well as for the prediction of extraction rates for corresponding salts. Experimental Section Materials. LiCl (purum, p.a., Fluka) and tetrabutylammonium tetraphenylborate (Bu,NPh4B) or tetraphenylarsonium 3,3-com‘On leave from Pad. Hochschule ‘N.K. Krupskaja”, Krollwitzer Str. 44. Halle 4050, G.D.R.

0022-365418912093-8204$0 1.5010

mo-bis(undecahydr0- 1,2-dicarba-3-cobalta-closo-dodecaborate) (Ph4AsDCC) were used for preparation of base-electrolyte solutions in double-distilled water and nitrobenzene (puriss., pea., Fluka). Tetraalkylammonium and trimethylalkylphosphonium tetraphenylborates (R4NPh4B,Me3RPPh4B)and N,N’-dialkyl4,4’-dipyridinium bis(tetrapheny1borate)s (R,V(Ph,B),), with R = methyl (Me), ethyl (Et), propyl (Pr), or butyl (Bu), were precipitated from corresponding quaternary ammonium or phosphonium hallogenides and sodium tetraphenylborate (Fluka). The product of this precipitation was recrystallized twice from acetone or water-acetone mixture. Ph4AsDCC and N,N’-dialkyL4,4’-dipyridinium dibromides were prepared as described in ref 11 and 12, respectively. LiC104, tetrabutylammonium perchlorate, tetraphenylarsonium chloride, and tetraalkylammonium chlorides and bromides, all purchased from Fluka as Reagent Grade chemicals, were used as received. The generous gift of trimethylalkylphosphonium bromides and iodides from Dr. M. Heinze, VEB Fahlberg-List Magdeburg (G.D.R.), is greatly acknowledged. Apparatus. A block scheme of the apparatus is shown in Figure 1. A flat water-nitrobenzene interface with a geometric area of 19.2 mm2 was formed in a four-electrode cell, which was described in detail e1~ewhere.l~The cell was immersed in a water ( I ) Mears, P. Faraday Discuss. Chem. SOC.1984, 77, 7. (2) Hanna, G. J.; Noble, R. D. Chem. Reu. 1985,85, 583. (3) Koryta, J. In The Interface Structure and Electrochemical Processes at the Boundary Between Two Immiscible Liquids; Kazarinov, V. E., Ed.; Springer Verlag: Berlin, 1987; p 3. (4) (a) Samec, Z.; Mardek, V.; Weber, J. J. Electroanal. Chem. Interfacial Electrochem. 1979, 100.841. (b) Samec, Z.; MareEek, V.; Korvta, J.; i(halil, M. W. J. Electroanal. Chem. Interfacial Electrochem. 1977,83, 393. (c) Hanzlik, J.; Samec, 2. Collect. Czech. Chem. Commun. 1987, 52, 830. (5) (a) Samec, 2.; MareEek, V.; Weber, J.; Homolka, D. J. Electroanal. Chem. Interfacial Electrochem. 1981,126, 105. (b) Samec, Z.; Mardek, V. J. Electroanal. Chem. Interfacial Electrochem. 1986, 200, 17. (c) Samec, Z.; Mardek, V.; Homolka, D. J. Electroanal. Chem. Interfacial Electrochem. 1983, 158, 25.

(6) (a) Gavach, C.; d’Epenoux, B.; Henry, F. J. Electroanal. Chem. Interfacial Electrochem. 1975, 64, 107. (b) Melroy, 0. R.; Buck, R. P. J. Electroanal. Chem. Interfacial Electrochem. 1982, 136, 19. (7) (a) Osakai, T.; Kakutani, T.; Senda, M. Bull. Chem. SOC.Jpn. 1984, 57, 370. (b) Osakai, T.; Kakutani, T.; Senda, M. Bull. Chem. Soc. Jpn. 1985, 58. 2626. (8) Buck, R. P.; Bronner, W. E. J. Electroanal. Chem. Interfacial Electrochem. 1986. 197. 179. (9) Kakiuchi, T.: Senda, M. Bull. Chem. SOC.Jpn. 1983, 56, 1753. (IO) Wandlowski, T.; MareEek, V.; Samec, 2. J. Electroanal. Chem. Interfacial Electrochem. 1988, 242, 291. (1 1) JanouSek, Z.; PleSek, J.; HeimLnek, S.; Base, K.; Todd, L. J.; Wright, W. F. Collect. Czech. Chem. Commun.1981, 46, 2818. (12) Evans, A. G.; Evans, J. C.; Baker, M. W. J. Chem. SOC.,Perkin Trans. 1911, 2, 1787. ( I 3) MareEek, V.; Samec, Z. J. Electroanal. Chem. Interfacial Electrochem. 1985, 185, 263.

0 1989 American Chemical Society

Electrochemical Kinetics at Liquid-Liquid Interfaces

TABLE I: Thermodynamic, Transport, and Kinetic Data for Transfer of Mono- and Divalent Ions across Water-Nitrobenzene Interface at 293 K" go",o, 106DW, 10600, 102k,,,0, cm2 s-I mV em2 s-I ion cm s-' cyapp 0.58 3.7 13.6 9.5 Me4N+ 27 9.0 0.64 9.3 4.0 Et,N+ -67 3.4 13.6 0.60 Pr,N+ -170 8.5 0.55 3.7 14.8 8.8 Me4P+ 9 12.6 0.51 3.6 -20 8.1 Me3EtP+ 3.1 12.6 0.58 -50 6.7 Me3PrP+ 8.9 0.57 2.9 -84 5.8 Me3BuP+ 2.7 8.3 0.56 39 6.1 pi-* -83 15.3 6.7 9.0 0.57 clod4.8 0.50 Me2V2+ -15 5.6 2.3 -4 3 4. I 1.5 5.3 0.49 Et2V2+ 6.8 0.55 Pr2V2+ -58 3.3 0.9

RE2

*p

The Journal of Physical Chemistry, Vol. 93, No. 25, 1989 8205

n

YR2 "ase electrolytes: 0.05 M LiCl in water, 0.05 M Bu4NPh4B (or 0.05 M Ph4AsDCC for Pr4N+ ion transfer) in nitrobenzene. bData taken from ref 10. Ag AgCl 0.05

M

LiCl + xMX2 (w)

0.05 M Bu4NC1 Bu4NPh4Bor Ph4AsDCC + or Ph,AsCI yMX2

0.05 M

(0)

AgCl Ag'

(w')

wherej = (-1)1/2, w is the angular frequency, C, is the differential capacitance of the double layer, X = Z,"(Z,,'- RJI and Z,,' or Z,," are the real and the imaginary parts of the measured impedance 2,. The ?ohtion resistance R, was fo_und as the highfrequency limit of Z,. The faradaic impedance Z,, was calculated from the admittance Ff,corresponding to the Xzion transfer7a

Ffl= Fl - F, where TI and sistance R,

(4)

Foare admittances corrected for the solution re-

y;' =

Z/ ( Z ; - R,)'

i=O, 1

+ Zr2

Results Potentiometry. In the case when the bulk concentrations 8*w and &O of the ion Xzin the aqueous and organic phase differ from zero, the Nernst potential E E = Eo

+ ( R T / z F ) In (co~o/co,w)+ AE"

(7)

should be established in the galvanic cell, which would correspond to the equilibrium in the ion-transfer reaction. Here Eo is the standard potential difference A:qo for the transfer of the ion Xz referred to that for the reference ion R; Le., Eo = A:qo - bWq Ro (cf. eq 2). The activity coefficient term AE"now includes contributions from the activity coefficients of the transferred ion Xz in water and nitrobenzene, which in the case of monovalent cations compensate for AE',Le., AE"= 2 mV, whereas for divalent cations AE" = -10 mV and for monovalent anions AE"= 12 mV, as estimated from the extended Debye-Huckel equation. Potentiometric measurements were carried out under conditions that (a) the total ion concentration ( x y ) or (b) the ion concentration in one phase only ( x or y ) were held constant and equal to 10" mol dm-3. The concentration ratio b / x ) was varied by changing ion concentrations x and/or y in the range IO4-lO-' mol dm-3. Figure 2 shows plots of the equilibrium potential The linear regression difference A:q as a function of In (8*o/&w). analysis of these plots yields the slopes in the range from 24.5 to 25.5, -23.0 to -25.0, or 13.2 to 13.4 mV/decade for monovalent cations, monovalent anions, or divalent cations, respectively, with the correlation coefficient in the range 0.98-0.99. Values of standard potential differences Atqo evaluated for monovalent ions from these plots are summarized in Table I. The evaluation of standard potential differences for divalent cations is a more complicated task. In contrast to monovalent

+

(14) Samec, Z.; MareEek, V.;Homolka, D. Faraday Discuss. Chem. SOC. 1984, 77, 197. ( I 5 ) Koryta, J.; Vanpek, P.; Biezina, M. J. Electroanal. Chem. Interfacial Electrorhem. 1977, 75, 21 1.

(16) MareEek, V.;Samec, Z. J . Electroanal. Chem. Interfacial Electrochem. 1983, 149, 185.

8206

The Journal of Physical Chemistry, Vol. 93, No. 25, 1989

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Wandlowski et al.

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Me.V"

I -01

1 1

I

/

1

J

I

I

I

-2

0

2

. I

In(cO."

c".-)

Figure 2. Equilibrium potential difference A:(p vs In for the interface between 0.05 M LiCl in water and 0.05 M Bu4NPh4Bor Ph4AsDCC in nitrobenzene in the presence of (A) monovalent cations, (B) monovalent anions, and (C) divalent cations.

ions studied, R2V2+cations form ion pairs with Ph4B- in nitrobenzene.4c Instead of the simple ion transfer, facilitated ion transfer takes place: e.g., in the case of the 1:l association" R2V2+(w) + Ph,B-(o) s R,VPh,B+(o)

(8) The standard potential Eo' = A r p o - A,WpoR or the standard potential difference A,"p0 for the simple transfer of R2V2+ion was evaluated from the equation Eo = Eo' - ( R T / 2 F ) In [ I

+ Koroco~o]+ A E "

(9)

where Eo is the equilibrium value of the potential E at co*O/co*w = 1 ; cf. eq 7 . The bulk concentration of the counterion Ph4B-

1

I

I

1

02

03

0 4 E.V

Figure 3. Voltammetric behavior of (A) monovalent cations ( 8 . O = 6 X lo4 mol d ~ n - ~ and ) (B) divalent cations (cosw = 4 X 10" mol dmV3)at the water-nitrobenzene interface at the scan rate of 50 mV s-I. Dashed line: voltammogram of base electrolytes for each case.

cove = 0.05 mol d ~ n - the ~ , activity coefficient of the RzV2+ion in nitrobenzene yo = 0.12 was estimated from the extended DebyeHiickel equation, and the association constants in nitrobenzene KO = 580, 648,or 611 dm3 mol-' for Me2V2+,EtzV2+,or Pr2Vz+, respectively, were taken from the literature.& Results of these evaluations are also in Table I. Cyclic Voltammetry. Figure 3 illustrates the voltammetric behavior of mono- and divalent cations observed for sweep rates of u = 5-100 mV s-I. Regardless of whether the ion Xzwas present in the aqueous (x # 0, y = 0 ) or nitrobenzene (x = 0, y z 0 ) phase, the peak current on the forward scan was proportional to both the square root of u and the ion concentration, while the peak potential difference was constant and equal to 58 f 2 mV or 29 f 2 mV for mono- and divalent cations, respectively. Diffusion coefficients Dw and DO of ions in water and nitrobenzene and were evaluated from voltreversible half-wave potentials El/2rev ammetric data by using the Nicholson-Shah theory." E l 2rcv was used to evaluate the standard potential Eo or the standard potential difference A,"qo, which agreed with potentiometric data, the difference being generally less than f 8 mV. Impedance Measurements. Typical impedance plots are displayed in Figure 4. Impedance plots for base electrolytes were smooth curves, which did not exhibit any faradaic or even kinetic control in the frequency range 0.4-1000 Hz. On the other hand, (17) Nicholson, R. S.; Shain, I. Anal. Chem. 1964, 36, 706.

The Journal of Physical Chemistry, Vol. 93, No. 25, 1989 8207

Electrochemical Kinetics at Liquid-Liquid Interfaces

TABLE II: Surface Charge Density and Components of Interfacial Potential Difference Based on CouyChapman or Modified Poisson-Boltzmann Theories (in Parentheses)' 6.0

2 .o

1.0

1.2

'.4 Z'.k n Figure 4. Impedance plots for the interface between 0.05 M LiCl in water and 0.05 M Bu4NPh4Bin nitrobenzene in the absence (0)or in the presence ( 0 )of Me3PrP+ion (cosw = c0*"= 5 X lo4 mol dm-)). Numbers on curves are frequencies in hertz.

0 3 t

02

c

i

t

I 1 -02

I

I

0

02

I I

E . Epzc,V

Figure 5. Differential capacitance of the double layer vs the potential at the interface between 0.05 M LiCl in water and 0.05 M Bu4NPh4B ( 0 )or Ph4AsDCC(0)in nitrobenzene.

the frequency region where the mass transport dominates was well-defined for the ion X2,cf. the unity-slope plot at frequencies lower than about 25 Hz. Above 25 Hz the system showed a frequency-limited kinetic region. At the highest frequencies all impedance plots merged and reached the high-frequency limit, which was determined by the solution resistance R, (2'= R,, 2" = 0). The characteristic U-shape of differential capacitance vs potential plots is apparent from Figure 5 . Capacitance data were independent of the frequency in the range 2.5-100 Hz, the scatter being less than 5%. Since the potential of zero surface charge Eprc(or the corresponding potential difference Atv zc) is known from the surface tension measurements: the surface cgarge density q can be evaluated by integrating the capacitance plot. Table I1 gives the results of this integration for the system consisting of 0.05 M LiCl in water and 0.05 M Bu4NPh4B in nitrobenzene, in which case E,, = 0.270 V (vs B U ~ N ' ) . ~Surface charge data represent the basis for an analysis of double-layer effects in

E? mV 160 180 200 220 240 260 270 280 300 320 340 360 380 400 420 440 460 480

AZ9, mV -110 -90 -70 -50 -30 -10 0 10 30 50 70 90 110 130 150 170 190 210

qw,

mCmT2 -22.0 -16.8 -12.4 -8.6 -5.1 -1.7 0 1.2 5.0 8.4 11.9 15.6 19.6 23.9 28.5 33.5 38.9 44.8

9;9

mV 39 (38) 31 (29) 23 (23) 14 (16) lO(11) 3 (4) 0 (0) -2 (-4) -10 (-10) -16 (-17) -22 (-22) -29 (-28) -35 (-35) -42 (-41) -48 (-48) -54 (-54) -60 (-58) -66 (-65)

9$

mV -54 (-44) -44 (-35) -34 (-28) -24 (-20) -15 (-12) -5 (-4) 0 (0) 3 (3) 14(12) 24 (20) 32 (26) 41 (33) 49 (40) 57 (47) 64 (53) 71 (59) 78 (65) 85 (71)

e9

mV -18 (-28) -16 (-26) -13 (-19) -11 (-14) -6 (-7) -2 (-2) 0 (0) 4 (4) 6 (8) 11 (14) 15 (22) 21 (28) 26 (35) 32 (42) 38 (50) 45 (58) 52 (66) 59 (75)

"Base electrolytes; 0.05 M LiCl in water, 0.05 M Bu4NPh4Bin nitrobenzene. b Referred to Bu4N+ion. ion-transfer kinetics as discussed later. Results of surface tensiong and impedancela measurements suggest that the modified Verwey-Niessen (MVN) modellg offers a plausible picture of the interface between two immiscible electrolyte solutions (ITIES). According to this model a layer of solvent molecules (the inner layer) separates two ionic space charge regions (the diffuse double layer). The interfacial potential difference splits into three contributions where cpi = cp(xy) - cp(xi) is the potential difference across the inner layer, i.e., between the hypothetical planes x; and x i separating the inner layer from the space charge regions, and CpZ" = cp(xy) - cp(w,bulk) and p i = cp(xi) - cp(o,bulk) are the potential differences across the space charge regions in the aqueous or the organic solvent phase. The ion distribution function and the components of the interfacial potential difference were calculated by means of the Gouy-Chapman (GC)20,21and modified Poisson-Boltzmann (MPB)22theories. In the former case the calculations are relatively straightforward.18 In the latter case we applied the MPB 4 version and the numerical procedure22 for a primitive model electrolyte, which consisted of a continuum dielectric medium containing spherical ions of radii r L = 0.2125 nm or ryon = 0.425 nm. The two space charge regions were considered as not overlapping, but the image forces were included. Results of these calculations are summarized in Table 11. As expected,23the G C theory somewhat overestimates the potential difference across the space charge region. However, at the charge densities encountered here, the discrepancies between these two theories are rather small and in the case of water practically negligible. It is evident that the interfacial potential difference is spread mainly in the diffuse double layer. Formal kinetics of the simple ion transfer is based on the first-order rate law I / z F S = zcw - f c o w h p e I is the electrical current, S is the interfacial area, and k' or k are the apparent rate constants of the ion transfer from the (18) Samec, Z.; MareEek, V.; Homolka, D. J . Electroanal. Chem. Interfacial Electrochem. 1985, 187, 31. (19) (a) Gavach, C.; Seta, P.; d'Epenoux, B. J . Electroanal. Interfacial Electrochem. 1977, 83, 225. (b) Reid, J. D.; Melroy, 0. R.; Buck, R. P. J . Electroanal. Chem. Interfacial Electrochem. 1983, 147, 7 1. (20) Gouy, G. C.R. Acad. Sci. 1910, 149, 654. (21) Chapman, D. L. Philos. Mag. 1913, 25, 475. (22) Outhwaite, C. W.; Bhuiyan, L. B.; Levine, S . J . Chem. SOC.,Faraday Trans. 2 1980, 76, 1388. (23) Carnie, S. L.; Torrie, G. M. Adu. Chem. Phys. 1984, 56, 141.

8208 The Journal of Physical Chemistry, Vol. 93, No. 25, 1989 I

Wandlowski et al. ---I--

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A

-

-05

Pr,Nt

E, .

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3

-1

0.1

0.5

0.3 u-lll,

s-112 I

Figure 6. Plot of the real (0)and the imaginary (0)components of the faradaic impedance vs w-I/* for the transfer of Me3EtP+ across the interface between 0.05 M LiCl water and 0.05 M Bu4NPh4B in nitrobenzene.

I

B PI-

-0.5

?

aqueous to the organic solvent phase or the reverse. The rate constants are related to each other

k' = k' exp(-AG/RT)

= k' exp[zF(E - Eo)/RT]

(12)

where A 6 is the apparent reaction Gibbs energy. Equation 12 ensures that the Nernst potential (eq 7) will establish under equilibrium conditions ( I = 0). Since the transport of the ion X' in the solution is obviously controlled by the linea: and semiinfinite diffusion, the corresponding faradaic impedance 2, can be written as the sum of the charge-transfer resistance & and the Warburg impedance ZwZs

Z,,= Rct + 2,

= R,,

+ (1 - j ) p ~ - ' / ~

I

I

-1

(13)

where -02

I

and the transport parameter is defined as

-0 1

0

I

01

I

C PryV"

Er,V"

Me,V"

5

tz

3 As follows from eq 13, plots of the real-Zjl and the imaginary 2';' parts of the faradaic impedance Z,,vs w - I / * should give straight lines with an equal slope of p and with intercept8 of Z',, = Rct and Z';,= 0, respectively. This was actually the case for all the ion-transfer systems measured. Typical plots are shown in Figure 6. Extrapolated values of Z;,at w-Il2 = 0 were then used tqevaluate the rate constant k through eq 14. Since plots of log k vs the equilibrium potential E gqve straight lines (Figure 7), two kinetic parameters were chosen to characterize the formal kinetics of the sipple ion _transfer, namely the apparent rate constant koapp= k ( E o ) = k(Eo) at the standard potential E = E O , and the apparent charge-transfer coefficient aaPp = (RT/zF)(a In i / a E )

-1.0

-

-1.5

-

(16)

Their values are summarized in Table I .

Discussion Thermodynamics and Transport. The standard potential of the simple ion transfer is related to the standard difference A:,'

1

- 0.1 (24) Samec, 2.J . Electroanal. Chem. Interfacial Electrochem. 1979, 99,

197. (25) Sluyters-Rehbach,M.; Sluyters, J. H. In Comprehensiue Treatise of Electrochemistry; Yeager, E.;Sarangapani, S.; Eds.; Plenum Press: New York, 1984; pp 177-292.

0 A:CP.V

Figure 7. Apparent rate constant vs the potential difference Arv for the transfer of (A) monovalent cations, (B)monovalent anions, and (C) divalent cations from the solution of 0.05 M LiCl in water to the solution of 0.05 M Bu,NPh4B or Ph4AsDCC in nitrobenzene.

The Journal of Physical Chemistry, Vol. 93, No. 25, 1989 8209

Electrochemical Kinetics at Liquid-Liquid Interfaces

c = 6/[(3rs/2rion) + 1/(1 + rs/rion)l (19) Obviously, when the size of the solvent is much smaller than that of the ion, so that the solvent can be considered as the hydrodyA:9" = A ~ O , J Z F (17) namic continuum, the numerical factor c = 6. The ion radius rion was calculated by eq 18 and 19 from diffusion coefficient in water Evaluation of either of these quantities from partition, solubility, (Table I) for the radius of water molecule rw = 0.155 nm. The or electrochemical measurements is inevitably based on an exformer was found to correlate with the ion radius Tion derived from trathermodynamic hypothesis. The assumption that Ph4As+ and molar volumes. In particular, the ratio Tion/rionis close to unity Ph4B- have equal Gibbs energies of transfer between any pair of and equals to (in parentheses ion radii from molar volumes36in solventsz6 (-35.9 kJ mol-' in water-nitrobenzene system27) has nm): 0.81 (0.258), 0.95 (0.310), 1.01 (0.352), or 1.08 (0.245) been widely used28and underlies the present discussion too. In for Me4N+, Et4N+, Pr4N+, or C104-, respectively. Moreover, addition to the Ph4As+ ion, the Bu4N+ ion has often been used except for Pr2V2+the ratio of diffusion coefficients D W / Pfor all as the reference ion in electrochemical studies, for which the standard potential difference A:cpo = -0,248 V was c a l c ~ l a t e d ' ~ ~ ~other ~ ions falls in the range 2.0-2.6, Le., not far from the ratio of viscosity coefficients for pure solvents, qo/vw = 2.03. from partition data.27 The latter value has been correctedI4 by Apparent Ion-Transfer Rates. On the basis of present results taking hWpo= -0.275 V, on the basis of which much better we conclude that the ion transfer across the ITIES is rather fast. agreement was reached between electrochemical data and those (in cm Somewhat lower values of the apparent rate constant pap derived from partition measurements. An independent experis-') for Me4N+ (6.5 X Et4N+ (3.7 X 10-2),SbP r 4 b (2.6 mental test of "Ph4AsPh4B" hypothesis is provided by measureX 10-2),5band Pi- (3.7 X 10-2)7bhave been derived from potential ments of the zero-charge potential Epzc.30 The point here is that sweep measurements. Here, the uncompensated ohmic potential the potential difference A:p across the water-nitrobenzene indrop is probably the main source of the experimental error. terface is spread mainly in the diffuse double layer;9,14*'8*'9 Le., Moreover, the change in the position and the shape of the interface when the surface charge density is zero (electrocapillary maxidue to the potential dependence of the surface tension9 can give mum), the potential difference A:cp should be close to zero too. rise to an additional ohmic potential drop, or to the convective In fact, by using the hypothesis above, the value of A:9p2c = 0 contribution to the ion transport.IO Apparent rate constants for was derived from surface tension9J9 or impedance14J8measurethe Me4N+(5.6 X 104)$6 Et4N+(2.3 X 10-3),6aand Pr4N+ (2.1 ments in the presence of various electrolytes in water and nitroX 10-3)6aion transfer have been obtained without properly taking benzene. into account the existence of the solution resistance and are quite From the present voltammetric or potentiometric measurements incorrect. Surprisingly, the preliminary results of equilibrium the following values of AGO,, (in kJ mol-') were obtained for impedance measurements8 also indicate rather slow ion transfer Me4N+,Et4N+,Pr4N+,Pi- (picrate), and C l o y , which agree well cm s-l. However, with the apparent rate constant about 5 X with partition dataz7(in parentheses): 2.9 (3.4), -6.4 (-5.7), -15.6 the use of platinum wires as reference electrode^^*^^ can be the (-15.7),35-4.1 (-4.6), and 7.9 (KO), respectively. Standard Gibbs source of error, because the easy polarization of the platinum energies of transfer 0.9, -1.9, -4.8, and -8.1 kJ mol-' were found electrodes can lead to a pseudokinetic behavior. analogously for Me4P+, Me3EtP+, Me3PrP+,and Me3BuP+ions, Effect of Electrical Double-Layer Structure. The diffusion for which no partition data are availcble. By taking into account double layer is rapidly e ~ t a b l i s h e dand ~ ~kinetic effects connected the ion association, the values of AGO,, = 2FA:p0 for Me2V2+, with its relaxation are far beyond the detection limit (> 1 ms) of Et2V2+,and Pr2V2+were -2.9, -8.3, and -1 1.2 kJ mol-', represent impedance measurements. Consequently, a slow step spectively. which would account for the kinetic behavior observed here must Obviously, the standard Gibbs energy of transfer reflects an be located in the inner-layer region. The three-step (or fourascending hydrophobic character of ions as the number of CH, position) mechanism of the simple ion transfer across the ITIES groups in the aliphatic carbon chains increases. Its structureappears to be a good approximation additive property is illustrated by almost identical average defast rds crements of -2.4, -3.1, or -2.1 kJ per CH2 group in R4N+, X2(w,b) Xz(w,xF) X2(o,xs) z% Xz(o,b) (20) Me3RP+, or R2VZ+homologous series. These results agree well with the values of -2S3, or -2.633 kJ per CH2 group reported where b denotes the bulk of the solution. The rate-determining previously for the RIR2R3R4N+series. step (rds) in this sequence is the ion jump over the inner layer Diffusion coefficients of ions in water, and analogously those (xy x;). The four-position mechanism of solute transfer across in nitrobenzene, show no striking difference and seem to reflect the liquid-liquid interface was proposed by The existence primarily the size of ions and the viscosity of the medium. Such of the space charge distribution in the double layer was considered a behavior is predicted by an Einstein-Stokes type of e q ~ a t i o n , ~ - ~ and ~ the Frumkin-type correction of the apparent rate constant namely for a spherical ion of radius rion was introduced later.24,40 This correction can be written as24

Gibbs energy of ion transfer from water to organic solvent A G O , , by

-

D = kT/c?rvrion

(18)

where kT is the Boltzmann factor and 11 is the viscosity coefficient (1.005 or 2.03 CPat 293 K for water or nitrobenzene, respectively). Provided that both ion and solvent are spherical, c is predicted to depend on the ratio of radii rs/rionof solvent and ion according to the simple r e l a t i o n ~ h i p ~ ~ (26) Parker, A. J. Chem. Reo. 1969, 69, 1. (27) Rais, J. Collect. Czech. Chem. Commun. 1971, 36, 3253. (28) Marcus, Y. Pure Appl. Chem. 1983, 55, 977. (29) Hung,Le. Q.J . Electroanal. Chem. Interfacial Electrochem. 1980, 115, 159. (30) Girault, H. H.J.; Schiffrin, D. J. Electrochim. Acta 1986, 31, 1341. (31) Abraham, M. A. J . Chem. Soc., Perkin Trans. 2 1972, 1343. (32) Osakai, T.; Kakutani, T.; Nishiwaki, Z.; Senda, M. Bunseki Kagaku 1983, 32, E81. (33) Iwamoto, E.; Ito, K.; Yamamoto, Y. Z . Phys. Chem. 1981,85, 894. (34) Robinson, R. A,; Stokes, R. H. Electrolyte Solutions, 2nd ed.; Butterworths: London, 1959; pp 43 and 125. (35) (a) Gierer, A.; Wirtz, K. Z . NaturJorsch. A 1953.8, 522. (b) Spemol, A.; Wirtz, K. Z . Naturforsch. A 1953, 8, 532.

i

= &g(xF) (21) where itis the rate constant for the rate-determining step and g(xy) is the ion distribution function at the outer Helmholtz plane on the aqueous side of the interface. By use of the GC theory for the MVN model, g(xy) can be expressedIga p; = - ( R T / z F ) In g(x;)

where p = (coco~O/cwco~w)l~z, e's are dielectric constants, and co's are base electrolyte concentrations. When the potential depen(36) Abraham, M. H.; Liszi, J. J . Inorg. Nucl. Chem. 1981, 43, 143. (37) Melroy, 0. R.; Bronner, W. E.; Buck, R. P. J . Electrochem. SOC. 1983, 130, 313. (38) Macdonald, J . R. Trans. Faraday Soc. 1970,66, 943. (39) Buck, R. P. Crit. Reu. Anal. Chem. 1975, 5 , 323. (40) d'Epenoux, B.; Seta, P.; Amblard, G.; Gavach, C. J . Electroanal. Chem. Interfacial Electrochem. 1979, 99, 71.

8210

The Journal of Physical Chemistry, Vol. 93, No. 25, 1989

Wandlowski et al.

applies to ions of various structyes a_nd charge numbers. Figure 8 presents plots of log k,vs AG, for all ions studied. The MPB values for cp; and cp, in eq 21 to 23 were taken from Table 11. Kinetic data for the Pi- ion transfer were taken from ref 10. When a particular ion_-trasferreaction is inspected, it is clear that changes in AG, and k, are rather small to provide a meaningful correlation. This is because the in_ner-layerpotential difference cpi or the Gibbs energy change AG, (eq 23) is not very sensitive to variations in the potential E . On the other hand, th_e kinetic data for various ions, which differ considerably in AG, due to different Gibbs energies of ion transfer, fall on a single straight line with the slope correspo_ndingto the true charge-transfer coefficient at = -RT(a In k,/dAG,) = 0.47, 0.40, or 0.58 for tetraalkylammonium, trimethylalkylphosphonium, and dialkyldipyridinium ions, respectively. To some degree of uncertainty, rate constants for individual ion-transfer reactions display analogous trends, e.g., for the picrate ion transfer the value of at = 0.6 f 0.1 was reported.’O The structure and the charge number of the ion s5em to influence the ion-transfer rate mainly indirectly through AG,. Various kinetic models of the rate-determining step have been proposed.6b~24~42-45 Melroy and Buclfb used the transition-state theory to express the rate constant k, by I I it = ko exp(-AG*,/kT) = ~ ( k T / hexp(-AG*,/kT) ) (24) B The standard Gibbs energy of activation A(?*, was divided into the chemical (AG*,) and electrical contributions and the latter was represented as some fraction of the electrical energy change across the inner layer: AG*,= AG*, + a,zFpi. Apart from the unclear physical meaning of the preexponential factor ~ ( k T / h ) , eq 24 does not predict the Brernsted-like corre1atio;shown in Figure 8, which is obviously implicit in the term AG*,. With reference to the transition-state theory Gf diffusion,& Girault and S ~ h i f f r i nused ~ ~ a similar expression for k,, but with ko = ( k T / h ) d , where d is the distance between two equilibrium positions of the ion. These authors have also_ introduc_ed the “chemical” charge-transfer coefficient a,,AG*, = &,AGO tr, which actually might control the slope of the plot in Figure 8. However, it should be noted that the question of validity of the rate equation, eq 24, remains unsolved within the framework of the transition-state theory. In fact, this type of expression can be derived for a 1 I molecular kinetic model based either on the tunnel hopping of 0 0.1 the ion from one cage formed by solvent molecules to the neighbor - A C c F‘,V cage47or on the nonadiabatic subbarrier penetration of an ion Figure 8. Correlation of the rate constant with the Gibbs energy of through the inner layer region.24 A more involved quantumion transfer across the inner layer AG, = -zF(p, - bWvo)for (A) momechanical treatment45shows that all these models could describe novalent and (B) divalent ions. Dashed line: linear regression for transfer processes of light ions (H’,Li+) or the processes occurring Me4Nt, Et4Nt, Pr4Nt, CIO,, and Pi- ions. Full lines: linear regressions in well-structured media, e.g., in solid ionic conductors. In liquids for Me4Pt (*), Me3EtPt (m), Me,PrPt (A), and Me3BuPt (V);or no well-defined initial and final states of an ion can be specified, Me2VZt, Et2VZt,and Pr2VZtions. and the meaning of the transition state and the Gibbs energy of activation for the transfer process becomes obscure. dence of i,is specified, eq 21 and 22 can be used to illustrate the effect of the double layer on the apparent rate c o n ~ t a n t . * * In ~ ~ * ~ ~ Hence, it seems more appropriate to treat the ion transport as the brownian motion by the stochastic method!8 Provided that particular, when the electrical part of the ion Gibbs energy change the characteristic frequency of ionic motion w is low, so that w across the inner layer AG, is negligible

I

x;

X

Figure 9. Schematic representation of the potential energy barrier to ion transfer across the inner layer (A) as the superposition of the linear potential connected with the long-range electrostatic interactions (B) and the barrier arising from the short-range repulsive interactions between the ion and solvent molecules in the inner layer (C).

and V = V ( x ) is the potential energy of the ion. The analytical solution has been obtained assuming that the transfer process is ~ t a t i o n a r y :a~p /~&~ = ~ ~0, J = constant. Actually, in that case the probability p takes the form of the Boltzmann equation: p s = const X exp(-V/kT). The potential energy V ( x ) of the ion in the inner layer was considered as a superposition of the potential energy barrier arising from the short-range repulsive interactions between ion and solvent molecules in the inner layer, and the linear potential connected with the long-range electrostatic interactions, inclusive of the contribution of the polar solvent around the ion (Figure 9)." The constant field treatment of the long-range interactions is somewhat an oversimplification, e.g., the resolvation may give rise to nonlinear effects. Near to its top, V ( x ) was approximated by the quadratic function of the ion coordinate x . The equation for the rate constant is then formally identical with eq 24,44where

ko = (mw*/,$*)Z= ( m w * / , $ * ) ( k T / 2 ~ m ) ' / ~(27)

A6*, = A @ + ( x * - xY)&lAv, + A p : / 2 m ~ * ~ d(28) ~ ) *the ]I/~ Z is the collision frequency, w* = [ ( l / m ) ( ~ 3 ~ V / a x ~ is frequency of the ion vibration at x = x * , d = x i - x? is the inner-layer thickness, AVt = V(xi)- V(xs) is the difference between the equilibrium potential energy prior to and after the jump, x* is the ion co_ordinate corIesponding to the potential energy maximum at_Aq = O,_andA P = V(x*)- V($) is the activation energy at AV, = 0. AV, is the sum of the resolvation energy and the elec@static energy change (zFq); Le., it is practically identical with A c t (eq 23). The frequency u* was estimated12 from the relationship (1/ 2 ) m ~ * ~ A= xkT, ~ where Ax is of the order of magnitude of intermolecular distances in liquids, e.g., Ax = 2rw = 0.310 nm. The friction coefficient was estimated as ,$*= k T / D w . For monovalent ions studied the frequency w* falls in the range (3.7-6.6) X 10" s-', and dimensionless hydrodynamic factor (mu*/,$*)is

B+(w)

+ A-(w)

G B+(o)

+ A-(0)

(29)

During the extraction process no electrical current flows through the system, i.e. I+ + I- = 0 (30) where I+ is the current corresponding to the cation and I- to the anion of a salt BA. In the course of this process the ratio of salt concentrations co/cw= co+/cw+= co-/cw-,and hence both the (cf. eq 7 ) and the ion-transfer interfacial potential difference hW9 rate I, (eq 1 1 ) vary till the equilibrium values of the distribution coefficient K0swor the distribution potential A:9,,istr are reached.49 For a 1:l BA salt50 KO," = ( c ~ ~ ~ / c ~ ~ " ) ( y O=~ / y W + ) exp[-(AGot,,+ + A60tr,-)/2RT] ( 3 1 ) and = (A~(PO++ 4 9 O - ) / 2

Ar(Pdistr

+ ( R T / 2 F ) ln

(Y~+YO-/YO+Y~-)

(32)

where denotes the equilibrium bulk concentration of the salt, ysiof ys* is the activity coefficient or the mean activity coefficient in the phase s. As shown in the previous section, the chargetransfer coefficient at = const = 0.5. The limiting rate of extraction of a 1:l BA salt from water to the organic solvent (P/cw = 0) is then given by (cf. also ref 49) I+/FS = h k o exp(rF&/RT) exp[fa,F(cpi

- A r p ) / R T ] c W= koVwcw( 3 3 )

where koSw is the extraction rate constant k 0 . W = (kO+kO-)'/2(KO*")*t

(34)

(49) Koryta, J.; Skalickg, M. J . Electroanal. Chem. Interfacial Electrochem. 1987, 229, 265. (50) Karpfen, F. M.; Randles, J. E. B. Trans. Faraday SOC.1953,49, 823.

J. Phys. Chem. 1989, 93, 8212-8219

8212

TABLE I V Thermodymmic and Kinetic Parameters of Extraction of Simple Salts from Water to Nitrobenzene

salt Me4NC104 Et4NC104 Pr4NC104 Me4NPi Et4NPi Pr4NPi

KO,"

0.1 13

0.728 5.07 1.27 8.16

56.8

A:q distr,

P,",

mV -28 -7 5

cm s-' 0.050 0.092

-124 33 -14 -63

0.253

0.147 0.269 0.737

and koi = ko exp(-Api/kr). Table IV lists values of distribution coefficients, distribution potentials, and extraction rate constants for a series of perchlorates and picrates, which were calculated from thermodynamic and kinetic parameters of individual iontransfer reactions obtained in this work. Since the constant koi is approximately the same for all ions, the leading factor in the extraction rate is the distribution coefficient KO-w. Our estimates

differ considerably from those previously reported.49 It should be noted that the authors49used a somewhat different set of values of ionic rate constants and an incorrect value of the standard potential difference for the picrate ion transfer. It is evident that the extraction of the simple salt from water to a high-permittivity solvent is a rather fast process, the kinetics of which is experimentally accessible only when a rapidly stirred system is used, enabling the separation of kinetic and transport contributions. No reliable experimental kinetic data on these processes have been reported. Registry No. Me4Nt, 51-92-3;Et,Nt, 66-40-0; Pr4Nt, 13010-31-6; Me4Pt, 32589-80-3; Me,EtP+, 79826-63-4; Me3PrPt, 44519-38-2; Me3BuPt, 122624-00-4;CIO,, 14797-73-0;Me2V2+,4685-14-7; Et2V2', 46713-38-6; Pr2VZt,46903-41-7; LiC1, 7447-41-8; Bu4NPh4B, 1552259-5; Ph4AsDCC, 76598-08-8; HzO,7732-18-5; Pi-, 14798-26-6; Me4NC104,2537-36-2;Et4NC104,2567-83-1; Pr4NCI04,15780-02-6; Me4NPi,733-60-8;Et4NPi,741-03-7; Pr4NPi, 747-43-3;nitrobenzene, 98-95-3.

Theoretical Nets with 18-Ring Channels: Enumeration, Geometrical Modeling, and Neutron Diffraction Study of AIP0,,-54 James W. Richardson, Jr.,*,t,*Joseph V. Smith,* and Joseph J. Plutht Department of Geophysical Sciences, The University of Chicago, Chicago, Illinois 60637, and IPNS Division, Argonne National Laboratory, Argonne, Illinois 60439 (Received: November 22, 1988; In Final Form: April 28, 1989)

The framework topology of aluminophosphate no. 54 is the same as that of the aluminophosphate-basedfamily of molecular sieves denoted VPI-5. It corresponds to that of theoretical net 81(1), now numbered 520, which has an 18-ring channel. Unit cell parameters for as-synthesized A1W4-54are a = 19.009 (2) A, c = 8.122 (1) A, V = 2541.63 AS.AlP04-54dehydrated at 275 "C has lattice parameters a = 18.549 ( I ) A, c = 8.404 (1) A, V = 2504.13 A3. The crystal structure of dehydrated A1P04-54 was determined from time-of-flight neutron diffraction data. The 13 theoretical nets with crankshaft chains that fit the hexagonal geometry and cell dimensions of A1P04-54 were considered as possible models for the structure. Only net 520 yielded a theoretical powder diffraction pattern that matched the data for A1P04-54. A Rietveld refinement for disordered AI,P in space group P63/mcm converged, but the uncertainties in distances and angles are high. The A1P04-54 framework contains tetrahedrally coordinated A1 and P at the vertices of a 3D net obtained by replacing each edge of a (4.4.18),(4.6.18), 2D net by a crankshaft chain. The average free diameter across the 18-ring channel is 12.5 A. (AI,P)-O bond distances from the Rietveld refinement range from 1.44 to 1.70 8, with a mean value of 1.60 A, and (A1,P)-0-(AI,P) angles range from 132 to 180O. Refinement assuming strict alternation of AI and P space group P 6 p n was unsuccessful because of strong pseudosymmetry. The diffraction patterns for the hydrated and dehydrated varieties of A1PO4-54 and for the aluminophosphate-based VPI-5 family are generally similar, but detailed variations of position and intensity indicate that structural changes deserve thorough study. For the present neutron diffraction data, Fourier analysis of a diffuse scattering component suggests weak association of water with framework oxygens, and incomplete dehydration.

Introduction Theoretical nets containing wide channels and windows are of considerable interest as the potential basis of molecular sieves for separation of large molecules, and for catalytic reactions involving heavy fractions of petroleum. Two infinite series of four-connected nets with unlimited ring size were invented by Smith and Dytrych,' and others have been described briefly, but not presented yet in detailed form (reviewed in ref 2). A new family of aluminophosphate-based molecular sieves containing pores defined by 18 tetrahedrally linked atoms was described by Davis et al.394 After completion of the present study, Crowder et aL5 published X-ray powder diffraction data for an uncalcined silicon-containing member that matches a theoretical pattern calculated for atomic positions based on the 81(1) net of Smith and Dytrych. Independently we examined the structure of A1PO4-54. We present a systematic enumeration of 13 theoretical structures with an 18-ring channel that generally fit the cell dimensions of both the Argonne National Laboratory.

$TheUniversity of Chicago.

VPI-5 family and A1PO4-54. Although the theoretical diffraction patterns are similar to each other, only the 8 1(1) net has space group symmetry that matches the systematic absences of the observed X-ray powder data of the VPI-5 family. We give a Rietveld refinement of pulsed-neutron diffraction data for a dehydrated powder of the new aluminophosphate A1P04-54 using a model based on the 81(1) topology. It was synthesized in accordance with the general procedures set forth in U.S.Patent 4310440 (ref 6) using a dialkylamine templating agent. The combined observations on the VPI-5 family and on A1PO4-54 demonstrate that they have the 81(1) framework topology in common. However, the names VPI-5 and A1P04-54 are retained (1) Smith, J. V.; Dytrych, W. J. Nature 1984, 309, 607-608. (2) Smith, J. V. Chem. Rev. 1988, 88, 149-182. (3) Davis, M. E.; Saldarriaga, C.; Montes, C.; Garces, J.; Crowder, C. Nature 1988, 331, 698-699.

(4) Davis, M. E.; Saldarriaga, C.; Montes, C.; Garces, J.; Crowder, C. Zeolites 1988, 8, 362-366. ( 5 ) Crowder, C. E.; Garces, J. M.; Davis, M. E. Ado. X-ray Anal., in press. (6) Wilson, S.T.; Lok, B. M.; Flanigen, E. M. U.S. Patent 4310440, January 1982.

0022-365418912093-8212$01.50/0 0 1989 American Chemical Society